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There are theories suggesting that the electrons and quarks are not elementary particles, but instead are composite particles of two or more yet undiscovered elementary particles. However experimentally we know the upper limits of the radii of these particles, and they are very small indeed. Any particles "inside" an electron would be confined to a very small volume. By Heisenberg's uncertainty principle, the particles inside would experience large fluctuations of momentum, making the total energy larger than the mass-energy of electron. Therefore the measured mass of the electron should actually be several orders of magnitude larger. This seems like a paradox.

How do composite-electron and composite-quark theories avoid this?

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  • $\begingroup$ not the best question(linked, not above), but this related question does have quite a good answer attached to it: physics.stackexchange.com/q/507454 $\endgroup$ – Alex Robinson Oct 15 '19 at 15:09
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    $\begingroup$ The fluctuations you imagine are virtual. How can the neutron decay involve a W when the mass of the W is 80 GeV and the mass of the neutron less than 1? It is all accommodated in the mathematics of the four vectors used in the theories. $\endgroup$ – anna v Oct 15 '19 at 15:37
  • $\begingroup$ The focus on hypothetical models of composite electrons/quarks may be a distraction, because the same line of reasoning leads to the same question in simpler cases. Consider QCD with the quark masses set to zero. In this model, pions are massless (because they're Goldstone bosons of the spontaneously broken chiral symmetry), even though they are composite in the sense that they don't correspond to any individual field in the QCD lagrangian. Would you agree that the same question also applies in this case? $\endgroup$ – Chiral Anomaly Oct 17 '19 at 13:04
  • $\begingroup$ Yes, it would. Since quarks are confined, there is a characteristic energy scale corresponding to them. Massless quarks with energy $E$ would have an effective mass $E/c^2$, which should make the pion to have an effective mass $2E/c^2$. Is this what you mean? $\endgroup$ – Zeick Oct 17 '19 at 13:41
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According to our currently accepted theory, the SM, electrons and quarks are elementary particles, pointlike, with zero spatial extension, and no substructure.

Now what you are suggesting, that the electron and quarks are not elementary, not pointlike and they do have a substructure, and some spatial extension could be based on two theories:

  1. preons

Basically the point of these models are reducing the large number of particles, explaining the three generations of fermions, calculate parameters not explained by the SM (mass, charge, color charge), explain large differences in energy masses, explain electroweak symmetry breaking without Higgs, explain neutrino oscillation.

https://en.wikipedia.org/wiki/Preon

  1. string theory

in this theory, pointlike particles are replaced by one dimensional strings.

In theories of particle physics based on string theory, the characteristic length scale of strings is assumed to be on the order of the Planck length, or 10−35 meters, the scale at which the effects of quantum gravity are believed to become significant.[15] On much larger length scales, such as the scales visible in physics laboratories, such objects would be indistinguishable from zero-dimensional point particles, and the vibrational state of the string would determine the type of particle.

https://en.wikipedia.org/wiki/String_theory

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